Then to find the true velocity at the end of T seconds and so forth, we take the integral of that, and we have:
(2) V=1/2RT2
To get the distance covered in T seconds at R rate of change, we integrate once more and come up with ... ah, let's see—Oh, sure:
(3) D=1/6RT3
Is that clear?"
"I'd like to see that one worked out on a blackboard," said Jimmy. "At the present, I'll take your word for it. What I'm interested in right now is: does this factor 'R' increase with the power setting?"
"Drake just lifted it to thirty feet per," said Hammond, "and I've been timing it. So far, it does."
"Steve," said McBride, "if we can figure out some way of keeping ourselves from getting killed as the acceleration hits the upper brackets, we'll have a drive that will get us places like fury. Think fast, brother."
Hammond looked up, just as the acceleration reached a peak, and it snapped his head sharply. "Whew," he said. "This is fine stuff, but we couldn't run anywhere very long this way. We'd shake the whole crate loose." He was thoughtful for a minute. "Don't suppose that blackboard mind of yours could figure out our course constants from this saw-toothed curve we're running?"
"Sure," grinned McBride. "Since the thing is not increasing constantly, but is returning to zero accel each time and then building up linearly to peak, our over-all, long-time acceleration is equivalent to the average acceleration. Besides, what difference does it make? We'll get there somehow, and we can probably plot well enough to keep from doing a lot of return-chasing to hit the lens."